The proposal includes a request for an external antitrust monitor paid for by Apple. The job of the monitor would be "to ensure that Apple's internal antitrust compliance policies are sufficient to catch anticompetitive activities before they result in harm to consumers," according to a Justice Department news release.

The monitor would work with an internal compliance officer, whom Apple would be required to hire. The compliance officer would report to Apple's board audit committee.

"The court found that Apple's illegal conduct deprived consumers of the benefits of e-book price competition and forced them to pay substantially higher prices," said Bill Baer, assistant attorney general in charge of the Department of Justice’s antitrust division, in the news release. "Under the department's proposed order, Apple's illegal conduct will cease and Apple and its senior executives will be prevented from conspiring to thwart competition in the future."

In July, U.S. federal Judge Denise Cote ruled that Apple had conspired with five major publishers to raise e-book prices. The case stemmed from Apple's launch of its iBookstore in 2010, a major feature of its new iPad.

Last year, the Justice Department filed an antitrust lawsuit against Apple and the five publishers, claiming that in an effort to compete against Amazon.com, the players had created a kind of cartel that would allow them to charge higher e-book prices.

The five publishers subsequently settled, leaving Apple to face trial on its own. Apple has continued to insist it did nothing wrong and has vowed to appeal the ruling.

But in the meantime, the federal judge will schedule an additional hearing to consider remedies against Apple.

In addition to the monitor, the Justice Department proposed that Apple's contracts with the publishers be terminated and that the company be prohibited from signing new ones for two years. Apple would still be able to sell e-books but would not be able to strike special deals with publishers.

The Justice Department also wants the judge to force Apple to let other e-book sellers, such as Amazon and Barnes & Noble, post links in their e-book apps that would take readers to their e-bookstores. Apple does not allow apps that run on the iPhone or iPad to link to external stores.